Add files using upload-large-folder tool

pretraining/mathematica/geometry/solids/10403.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.533 & 0.273 & 0.215 \\
+ 0.176 & 0.838 & 0.849 \\
+ 0.011 & 0.241 & 0.233 \\
+ 0.311 & 0.249 & 0.12 \\
+ 0.013 & 0.956 & 0.788 \\
+ 0.543 & 0.441 & 0.753 \\
+ 0.628 & 0.956 & 0.341 \\
+ 0.038 & 0.559 & 0.745 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.11$ 
+Solid Angle: $1.74$ 
+Surface Area: $1.49$

pretraining/mathematica/geometry/solids/10637.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.326 & 0.731 & 0.387 \\
+ 0.985 & 0.577 & 0.637 \\
+ 0.163 & 0.766 & 0.823 \\
+ 0.201 & 0.509 & 0.907 \\
+ 0.364 & 0.243 & 0.492 \\
+ 0.169 & 0.549 & 0.402 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.05$ 
+Surface Area: $0.89$ 
+Solid Angle: $1.81$

pretraining/mathematica/geometry/solids/1125.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -\frac{1}{4} \sqrt{2+\sqrt{3}} & \frac{1}{8} \left(\sqrt{2}-\sqrt{6}\right) & \frac{1}{2 \sqrt{2}} \\
+ -\frac{1}{4} \sqrt{2+\sqrt{3}} & \frac{\sqrt{2-\sqrt{3}}}{4} & -\frac{1}{2 \sqrt{2}} \\
+ -\frac{1}{2 \sqrt{2}} & -\frac{1}{2 \sqrt{2}} & -\frac{1}{2 \sqrt{2}} \\
+ -\frac{1}{2 \sqrt{2}} & \frac{1}{2 \sqrt{2}} & \frac{1}{2 \sqrt{2}} \\
+ \frac{1}{8} \left(\sqrt{2}-\sqrt{6}\right) & -\frac{1}{4} \sqrt{2+\sqrt{3}} & \frac{1}{2 \sqrt{2}} \\
+ \frac{1}{8} \left(\sqrt{2}-\sqrt{6}\right) & \frac{\sqrt{2+\sqrt{3}}}{4} & -\frac{1}{2 \sqrt{2}} \\
+ \frac{\sqrt{2-\sqrt{3}}}{4} & -\frac{1}{4} \sqrt{2+\sqrt{3}} & -\frac{1}{2 \sqrt{2}} \\
+ \frac{\sqrt{2-\sqrt{3}}}{4} & \frac{\sqrt{2+\sqrt{3}}}{4} & \frac{1}{2 \sqrt{2}} \\
+ \frac{1}{2 \sqrt{2}} & -\frac{1}{2 \sqrt{2}} & \frac{1}{2 \sqrt{2}} \\
+ \frac{1}{2 \sqrt{2}} & \frac{1}{2 \sqrt{2}} & -\frac{1}{2 \sqrt{2}} \\
+ \frac{\sqrt{2+\sqrt{3}}}{4} & \frac{1}{8} \left(\sqrt{2}-\sqrt{6}\right) & -\frac{1}{2 \sqrt{2}} \\
+ \frac{\sqrt{2+\sqrt{3}}}{4} & \frac{\sqrt{2-\sqrt{3}}}{4} & \frac{1}{2 \sqrt{2}} \\
+\end{array}
+\right)$. Determine the Centroid.
+Answer:
+$\{0,0,0\}$

pretraining/mathematica/geometry/solids/13225.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.953 & 0.843 & 0.735 \\
+ 0.082 & 0.661 & 0.148 \\
+ 0.01 & 0.05 & 0.314 \\
+ 0.673 & 0.636 & 0.158 \\
+ 0.417 & 0.901 & 0.832 \\
+ 0.634 & 0.498 & 0.29 \\
+ 0.316 & 0.893 & 0.945 \\
+ 0.719 & 0.566 & 0.784 \\
+ 0.048 & 0.453 & 0.111 \\
+ 0.812 & 0.919 & 0.21 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.94$ 
+Volume: $0.17$ 
+Solid Angle: $1.18$

pretraining/mathematica/geometry/solids/14573.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.829 & 0.996 & 0.191 \\
+ 0.885 & 0.411 & 0.785 \\
+ 0.197 & 0.295 & 0.687 \\
+ 0.955 & 0.742 & 0.28 \\
+ 0.817 & 0.772 & 0.215 \\
+ 0.386 & 0.582 & 0.421 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $0.82$ 
+Solid Angle: $0.46$ 
+Volume: $0.02$

pretraining/mathematica/geometry/solids/15700.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.424 & 0.826 & 0.876 \\
+ 0.664 & 0.373 & 0.057 \\
+ 0.789 & 0.416 & 0.182 \\
+ 0.82 & 0.491 & 0.524 \\
+ 0.923 & 0.352 & 0.587 \\
+ 0.111 & 0.926 & 0.795 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.02$ 
+Surface Area: $0.81$ 
+Solid Angle: $0.44$

pretraining/mathematica/geometry/solids/19583.txt

@@ -0,0 +1,77 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} \\
+ -\frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{1}{2} \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ 0 & \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ 0 & \frac{1}{4} \left(5+3 \sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ 0 & \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ -\frac{1}{2} & 0 & \frac{1}{4} \left(-5-3 \sqrt{5}\right) \\
+ 0 & \frac{1}{4} \left(-5-3 \sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{1}{2} \\
+ -\frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{2} & 0 & \frac{1}{4} \left(-5-3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ -\frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(-1-\sqrt{5}\right) \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(5+3 \sqrt{5}\right) & \frac{1}{2} & 0 \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-3 \sqrt{5}\right) & -\frac{1}{2} & 0 \\
+ \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-5-3 \sqrt{5}\right) & \frac{1}{2} & 0 \\
+ \frac{1}{2} \left(1+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} \\
+ \frac{1}{4} \left(5+3 \sqrt{5}\right) & -\frac{1}{2} & 0 \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -\frac{1}{2} & \frac{1}{2} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{2} \left(-3-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \\
+ -\frac{1}{2} & 0 & \frac{1}{4} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(-1-\sqrt{5}\right) & \frac{1}{4} \left(3+\sqrt{5}\right) \\
+ -\frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{1}{2} & 0 & \frac{1}{4} \left(5+3 \sqrt{5}\right) \\
+ \frac{1}{4} \left(3+\sqrt{5}\right) & \frac{1}{2} \left(2+\sqrt{5}\right) & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{4} \left(-3-\sqrt{5}\right) & -1-\frac{\sqrt{5}}{2} & \frac{1}{2} \left(1+\sqrt{5}\right) \\
+ \frac{1}{2} & \frac{1}{2} \left(3+\sqrt{5}\right) & \frac{1}{4} \left(-3-\sqrt{5}\right) \\
+ \frac{3}{4}+\frac{13}{4 \sqrt{5}} & \frac{1}{2} & \frac{3}{10} \left(5+\sqrt{5}\right) \\
+ \frac{3}{4}+\frac{13}{4 \sqrt{5}} & -\frac{1}{2} & \frac{3}{10} \left(5+\sqrt{5}\right) \\
+ \frac{5}{4}+\frac{13}{4 \sqrt{5}} & \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{20} \left(25+\sqrt{5}\right) \\
+ 1+\frac{9}{2 \sqrt{5}} & 0 & \frac{1}{20} \left(15+\sqrt{5}\right) \\
+ \frac{5}{4}+\frac{13}{4 \sqrt{5}} & \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{20} \left(25+\sqrt{5}\right) \\
+ -\frac{3}{4}-\frac{13}{4 \sqrt{5}} & \frac{1}{2} & \frac{3}{10} \left(5+\sqrt{5}\right) \\
+ -\frac{3}{4}-\frac{13}{4 \sqrt{5}} & -\frac{1}{2} & \frac{3}{10} \left(5+\sqrt{5}\right) \\
+ -\frac{5}{4}-\frac{13}{4 \sqrt{5}} & \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{20} \left(25+\sqrt{5}\right) \\
+ -1-\frac{9}{2 \sqrt{5}} & 0 & \frac{1}{20} \left(15+\sqrt{5}\right) \\
+ -\frac{5}{4}-\frac{13}{4 \sqrt{5}} & \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{20} \left(25+\sqrt{5}\right) \\
+\end{array}
+\right)$. Determine the SurfaceArea.
+Answer:
+$\frac{1}{2} \left(20+15 \sqrt{3}+50 \sqrt{5+2 \sqrt{5}}+\sqrt{5 \left(5+2 \sqrt{5}\right)}\right)$

pretraining/mathematica/geometry/solids/19870.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.682 & 0.384 & 0.234 \\
+ 0.935 & 0.431 & 0.951 \\
+ 0.851 & 0.177 & 0.746 \\
+ 0.877 & 0.579 & 0.577 \\
+ 0.028 & 0.474 & 0.714 \\
+ 0.14 & 0.181 & 0.526 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.09$ 
+Volume: $0.06$ 
+Solid Angle: $1.02$

pretraining/mathematica/geometry/solids/22420.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.738 & 0.808 & 0.683 \\
+ 0.777 & 0.329 & 0.728 \\
+ 0.913 & 0.51 & 0.611 \\
+ 0.407 & 0.9 & 0.938 \\
+ 0.779 & 0.559 & 0.047 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $0.68$ 
+Volume: $0.02$ 
+Solid Angle: $2.55$

pretraining/mathematica/geometry/solids/22547.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.138 & 0.392 & 0.973 \\
+ 0.808 & 0.238 & 0.18 \\
+ 0.781 & 0.944 & 0.931 \\
+ 0.789 & 0.5 & 0.52 \\
+ 0.212 & 0.96 & 0.716 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.06$ 
+Surface Area: $1.23$ 
+Solid Angle: $0.55$

pretraining/mathematica/geometry/solids/24321.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.207 & 0.901 & 0.595 \\
+ 0.976 & 0.894 & 0.99 \\
+ 0.244 & 0.157 & 0.405 \\
+ 0.989 & 0.635 & 0.494 \\
+ 0.474 & 0.953 & 0.299 \\
+ 0.419 & 0.759 & 0.285 \\
+ 0.305 & 0.316 & 0.728 \\
+ 0.722 & 0.034 & 0.351 \\
+ 0.835 & 0.273 & 0.756 \\
+ 0.51 & 0.972 & 0.892 \\
+ 0.621 & 0.332 & 0.893 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $2.08$ 
+Volume: $0.22$ 
+Solid Angle: $2.12$

pretraining/mathematica/geometry/solids/26253.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.984 & 0.386 & 0.72 \\
+ 0.269 & 0.492 & 0.843 \\
+ 0.225 & 0.936 & 0.221 \\
+ 0.755 & 0.315 & 0.816 \\
+ 0.334 & 0.997 & 0.966 \\
+ 0.248 & 0.333 & 0.198 \\
+ 0.925 & 0.457 & 0.432 \\
+ 0.734 & 0.862 & 0.461 \\
+ 0.315 & 0.927 & 0.045 \\
+ 0.474 & 0.214 & 0.082 \\
+ 0.967 & 0.44 & 0.954 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $2.55$ 
+Surface Area: $2.2$ 
+Volume: $0.23$

pretraining/mathematica/geometry/solids/26276.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.038 & 0.854 & 0.853 \\
+ 0.567 & 0.032 & 0.75 \\
+ 0.94 & 0.204 & 0.338 \\
+ 0.158 & 0.667 & 0.207 \\
+ 0.666 & 0.638 & 0.562 \\
+ 0.016 & 0.764 & 0.827 \\
+ 0.862 & 0.467 & 0.279 \\
+ 0.271 & 0.2 & 0.449 \\
+ 0.45 & 0.4 & 0.944 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.65$ 
+Solid Angle: $1.04$ 
+Volume: $0.14$

pretraining/mathematica/geometry/solids/2681.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.478 & 0.256 & 0.414 \\
+ 0.496 & 0.722 & 0.023 \\
+ 0.169 & 0.452 & 0.72 \\
+ 0.709 & 0.346 & 0.047 \\
+ 0.345 & 0.744 & 0.155 \\
+ 0.871 & 0.724 & 0.014 \\
+ 0.815 & 0.473 & 0.322 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $1.65$ 
+Surface Area: $0.88$ 
+Volume: $0.04$

pretraining/mathematica/geometry/solids/27848.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.251 & 0.382 & 0.863 \\
+ 0.619 & 0.288 & 0.291 \\
+ 0.909 & 0.965 & 0.848 \\
+ 0.677 & 0.37 & 0.809 \\
+ 0.825 & 0.193 & 0.387 \\
+ 0.335 & 0.289 & 0.596 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $0.91$ 
+Volume: $0.04$ 
+Solid Angle: $0.54$

pretraining/mathematica/geometry/solids/28086.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.248 & 0.749 & 0.539 \\
+ 0.334 & 0. & 0.487 \\
+ 0.127 & 0.216 & 0.882 \\
+ 0.632 & 0.57 & 0.057 \\
+ 0.671 & 0.913 & 0.278 \\
+ 0.568 & 0.112 & 0.54 \\
+ 0.721 & 0.458 & 0.864 \\
+ 0.562 & 0.043 & 0.899 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.57$ 
+Solid Angle: $1.69$ 
+Volume: $0.12$

pretraining/mathematica/geometry/solids/28570.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.691 & 0.649 & 0.727 \\
+ 0.808 & 0.123 & 0.345 \\
+ 0.366 & 0.364 & 0.653 \\
+ 0.88 & 0.14 & 0.983 \\
+ 0.612 & 0.68 & 0.92 \\
+ 0.433 & 0.39 & 0.81 \\
+ 0.648 & 0.82 & 0.094 \\
+ 0.664 & 0.398 & 0.961 \\
+ 0.363 & 0.553 & 0.15 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.1$ 
+Solid Angle: $5.17$ 
+Surface Area: $1.38$

pretraining/mathematica/geometry/solids/30401.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.346 & 0.984 & 0.993 \\
+ 0.943 & 0.364 & 0.754 \\
+ 0.244 & 0.022 & 0.508 \\
+ 0.403 & 0.797 & 0.13 \\
+ 0.711 & 0.678 & 0.048 \\
+ 0.836 & 0.419 & 0.554 \\
+ 0.907 & 0.492 & 0.993 \\
+ 0.233 & 0.038 & 0.761 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.18$ 
+Surface Area: $2.05$ 
+Solid Angle: $0.76$

pretraining/mathematica/geometry/solids/31232.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.63 & 0.464 & 0.652 \\
+ 0.319 & 0.517 & 0.376 \\
+ 0.844 & 0.592 & 0.732 \\
+ 0.88 & 0.57 & 0.656 \\
+ 0.004 & 0.729 & 0.2 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.$ 
+Solid Angle: $1.1$ 
+Surface Area: $0.3$

pretraining/mathematica/geometry/solids/32177.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.894 & 0.19 & 0.505 \\
+ 0.071 & 0.899 & 0.56 \\
+ 0.005 & 0.807 & 0.937 \\
+ 0.963 & 0.292 & 0.051 \\
+ 0.968 & 0.883 & 0.239 \\
+ 0.247 & 0.563 & 0.9 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.88$ 
+Surface Area: $1.61$ 
+Volume: $0.09$

pretraining/mathematica/geometry/solids/32186.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.414 & 0.3 & 0.51 \\
+ 0.951 & 0.128 & 0.502 \\
+ 0.511 & 0.929 & 0.96 \\
+ 0.837 & 0.223 & 0.471 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.15$ 
+Surface Area: $0.46$ 
+Volume: $0.$

pretraining/mathematica/geometry/solids/32500.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.007 & 0.121 & 0.156 \\
+ 0.729 & 0.932 & 0.337 \\
+ 0.927 & 0.755 & 0.795 \\
+ 0.693 & 0.186 & 0.546 \\
+ 0.268 & 0.091 & 0.393 \\
+ 0.861 & 0.522 & 0.919 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.15$ 
+Volume: $0.04$ 
+Surface Area: $1.22$

pretraining/mathematica/geometry/solids/32778.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.242 & 0.209 & 0.964 \\
+ 0.261 & 0.647 & 0.113 \\
+ 0.079 & 0.511 & 0.812 \\
+ 0.536 & 0.592 & 0.015 \\
+ 0.987 & 0.108 & 0.211 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.02$ 
+Surface Area: $1.22$ 
+Solid Angle: $0.16$

pretraining/mathematica/geometry/solids/33446.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.866 & 0.262 & 0.368 \\
+ 0.331 & 0.256 & 0.489 \\
+ 0.223 & 0.172 & 0.913 \\
+ 0.368 & 0.909 & 0.507 \\
+ 0.253 & 0.493 & 0.073 \\
+ 0.081 & 0.4 & 0.75 \\
+ 0.756 & 0.635 & 0.137 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.09$ 
+Surface Area: $1.36$ 
+Solid Angle: $0.86$

pretraining/mathematica/geometry/solids/35631.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.687 & 0.546 & 0.353 \\
+ 0.767 & 0.581 & 0.818 \\
+ 0.093 & 0.136 & 0.563 \\
+ 0.351 & 0.39 & 0.433 \\
+ 0.414 & 0.12 & 0.482 \\
+ 0.795 & 0.911 & 0.368 \\
+ 0.463 & 0.182 & 0.539 \\
+ 0.871 & 0.391 & 0.626 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.04$ 
+Surface Area: $0.84$ 
+Solid Angle: $3.47$

pretraining/mathematica/geometry/solids/36988.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.48 & 0.871 & 0.132 \\
+ 0.823 & 0.176 & 0.774 \\
+ 0.763 & 0.422 & 0.919 \\
+ 0.941 & 0.515 & 0.244 \\
+ 0.979 & 0.425 & 0.807 \\
+ 0.146 & 0.16 & 0.041 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.09$ 
+Solid Angle: $0.72$ 
+Surface Area: $1.41$

pretraining/mathematica/geometry/solids/37187.txt

@@ -0,0 +1,21 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -1 & 0 & -\frac{1}{2} \\
+ -1 & 0 & \frac{1}{2} \\
+ -\frac{1}{2} & -\frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ -\frac{1}{2} & -\frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ -\frac{1}{2} & \frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ -\frac{1}{2} & \frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ \frac{1}{2} & -\frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ \frac{1}{2} & -\frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ \frac{1}{2} & \frac{\sqrt{3}}{2} & -\frac{1}{2} \\
+ \frac{1}{2} & \frac{\sqrt{3}}{2} & \frac{1}{2} \\
+ 1 & 0 & -\frac{1}{2} \\
+ 1 & 0 & \frac{1}{2} \\
+ \frac{1}{4} \left(-3-\sqrt{6}\right) & \frac{1}{4} \sqrt{5+2 \sqrt{6}} & 0 \\
+ \frac{1}{4} \left(3+\sqrt{6}\right) & \frac{1}{4} \sqrt{5+2 \sqrt{6}} & 0 \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$26$

pretraining/mathematica/geometry/solids/37946.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.864 & 0.643 & 0.707 \\
+ 0.798 & 0.187 & 0.46 \\
+ 0.234 & 0.205 & 0.109 \\
+ 0.811 & 0.146 & 0.862 \\
+ 0.138 & 0.039 & 0.418 \\
+ 0.239 & 0.795 & 0.24 \\
+ 0.985 & 0.482 & 0.852 \\
+ 0.106 & 0.933 & 0.648 \\
+ 0.866 & 0.241 & 0.326 \\
+ 0.821 & 0.824 & 0.287 \\
+ 0.209 & 0.341 & 0.113 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $4.96$ 
+Surface Area: $2.22$ 
+Volume: $0.24$

pretraining/mathematica/geometry/solids/38952.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.915 & 0.736 & 0.564 \\
+ 0.244 & 0.426 & 0.83 \\
+ 0.14 & 0.188 & 0.033 \\
+ 0.716 & 0.685 & 0.879 \\
+ 0.312 & 0.883 & 0.047 \\
+ 0.151 & 0.104 & 0.593 \\
+ 0.202 & 0.522 & 0.024 \\
+ 0.105 & 0.703 & 0.657 \\
+ 0.357 & 0.999 & 0.52 \\
+ 0.861 & 0.174 & 0.022 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.27$ 
+Solid Angle: $2.01$ 
+Surface Area: $2.39$

pretraining/mathematica/geometry/solids/41691.txt

@@ -0,0 +1,20 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.073 & 0.959 & 0.309 \\
+ 0.026 & 0.947 & 0.271 \\
+ 0.867 & 0.348 & 0.47 \\
+ 0.226 & 0.43 & 0.866 \\
+ 0.075 & 0.153 & 0.059 \\
+ 0.235 & 0.509 & 0.019 \\
+ 0.687 & 0.195 & 0.493 \\
+ 0.196 & 0.983 & 0.628 \\
+ 0.024 & 0.829 & 0.414 \\
+ 0.773 & 0.662 & 0.872 \\
+ 0.832 & 0.911 & 0.709 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.22$ 
+Solid Angle: $4.03$ 
+Surface Area: $2.15$

pretraining/mathematica/geometry/solids/41966.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.947 & 0.154 & 0.043 \\
+ 0.593 & 0.374 & 0.313 \\
+ 0.469 & 0.345 & 0.77 \\
+ 0.238 & 0.894 & 0.61 \\
+ 0.029 & 0.901 & 0.423 \\
+ 0.262 & 0.852 & 0.991 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.13$ 
+Volume: $0.04$ 
+Solid Angle: $0.1$

pretraining/mathematica/geometry/solids/42211.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.763 & 0.511 & 0.768 \\
+ 0.261 & 0.115 & 0.742 \\
+ 0.216 & 0.37 & 0.172 \\
+ 0.032 & 0.892 & 0.75 \\
+ 0.537 & 0.926 & 0.002 \\
+ 0.78 & 0.944 & 0.231 \\
+ 0.126 & 0.078 & 0.974 \\
+ 0.276 & 0.272 & 0.372 \\
+ 0.229 & 0.852 & 0.954 \\
+ 0.981 & 0.795 & 0.476 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $2.38$ 
+Volume: $0.22$ 
+Surface Area: $2.26$

pretraining/mathematica/geometry/solids/42352.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.657 & 0.622 & 0.113 \\
+ 0.27 & 0.776 & 0.085 \\
+ 0.901 & 0.623 & 0.954 \\
+ 0.195 & 0.422 & 0.809 \\
+ 0.327 & 0.618 & 0.846 \\
+ 0.315 & 0.893 & 0.826 \\
+ 0.286 & 0.813 & 0.074 \\
+ 0.56 & 0.248 & 0.42 \\
+ 0.081 & 0.633 & 0.462 \\
+ 0.902 & 0.924 & 0.123 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $3.62$ 
+Volume: $0.18$ 
+Surface Area: $1.87$

pretraining/mathematica/geometry/solids/42724.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.879 & 0.199 & 0.1 \\
+ 0.935 & 0.754 & 0.894 \\
+ 0.824 & 0.686 & 0.244 \\
+ 0.625 & 0.191 & 0.835 \\
+ 0.144 & 0.754 & 0.575 \\
+ 0.676 & 0.851 & 0.455 \\
+ 0.424 & 0.185 & 0.58 \\
+ 0.436 & 0.577 & 0.181 \\
+ 0.584 & 0.523 & 0.952 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.93$ 
+Surface Area: $1.7$ 
+Volume: $0.17$

pretraining/mathematica/geometry/solids/43559.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.649 & 0.717 & 0.212 \\
+ 0.025 & 0.268 & 0.372 \\
+ 0.608 & 0.894 & 0.957 \\
+ 0.25 & 0.735 & 0.006 \\
+ 0.031 & 0.775 & 0.04 \\
+ 0.723 & 0.588 & 0.844 \\
+ 0.289 & 0.19 & 0.875 \\
+ 0.304 & 0.736 & 0.782 \\
+ 0.103 & 0.13 & 0.544 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $1.42$ 
+Volume: $0.13$ 
+Surface Area: $1.73$

pretraining/mathematica/geometry/solids/47225.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.482 & 0.827 & 0.444 \\
+ 0.717 & 0.09 & 0.571 \\
+ 0.422 & 0.168 & 0.335 \\
+ 0.611 & 0.35 & 0.147 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $0.43$ 
+Volume: $0.01$ 
+Solid Angle: $0.13$

pretraining/mathematica/geometry/solids/47674.txt

@@ -0,0 +1,5 @@
+Problem:
+An ellipsoid centered at $\{-9.009,9.625,7.589\}$ has radii $\{5.837,9.789,0.137\}$. Estimate the ellipsoid's surface area and volume.
+Answer:
+Surface Area: $359.59$ 
+Volume: $32.71$

pretraining/mathematica/geometry/solids/48383.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.098 & 0.215 & 0.079 \\
+ 0.058 & 0.243 & 0.075 \\
+ 0.113 & 0.525 & 0.941 \\
+ 0.43 & 0.314 & 0.796 \\
+ 0.057 & 0. & 0.121 \\
+ 0.285 & 0.692 & 0.914 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $0.72$ 
+Volume: $0.03$ 
+Solid Angle: $2.83$

pretraining/mathematica/geometry/solids/52500.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.255 & 0.973 & 0.532 \\
+ 0.882 & 0.463 & 0.099 \\
+ 0.075 & 0.908 & 0.084 \\
+ 0.727 & 0.489 & 0.875 \\
+ 0.676 & 0.071 & 0.175 \\
+ 0.366 & 0.683 & 0.812 \\
+ 0.249 & 0.31 & 0.835 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.84$ 
+Solid Angle: $1.64$ 
+Volume: $0.16$

pretraining/mathematica/geometry/solids/52600.txt

@@ -0,0 +1,6 @@
+Problem:
+A cone with radius $1.666$ has its base centered at$\{7.487,4.707,5.466\}$ and its tip is at $\{2.384,8.789,2.599\}$. Estimate the cone's surface area, volume, and centroid.
+Answer:
+Surface Area: $47.07$ 
+Centroid: $\{6.21,5.73,4.75\}$ 
+Volume: $20.74$

pretraining/mathematica/geometry/solids/54182.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.302 & 0.355 & 0.096 \\
+ 0.121 & 0.847 & 0.418 \\
+ 0.709 & 0.131 & 0.13 \\
+ 0.047 & 0.259 & 0.921 \\
+ 0.499 & 0.052 & 0.395 \\
+ 0.159 & 0.553 & 0.089 \\
+ 0.87 & 0.28 & 0.577 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $3.26$ 
+Surface Area: $1.49$ 
+Volume: $0.1$

pretraining/mathematica/geometry/solids/5442.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.499 & 0.866 & 0.059 \\
+ 0.823 & 0.843 & 0.148 \\
+ 0.371 & 0.642 & 0.134 \\
+ 0.827 & 0.205 & 0.124 \\
+ 0.193 & 0.327 & 0.793 \\
+ 0.693 & 0.276 & 0.329 \\
+ 0.625 & 0.971 & 0.294 \\
+ 0.301 & 0.236 & 0.814 \\
+ 0.12 & 0.565 & 0.91 \\
+ 0.058 & 0.643 & 0.357 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $2.34$ 
+Surface Area: $1.61$ 
+Volume: $0.11$

pretraining/mathematica/geometry/solids/56677.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.336 & 0.885 & 0.049 \\
+ 0.753 & 0.61 & 0.959 \\
+ 0.008 & 0.479 & 0.498 \\
+ 0.942 & 0.393 & 0.521 \\
+ 0.427 & 0.814 & 0.776 \\
+ 0.428 & 0.751 & 0.832 \\
+ 0.584 & 0.164 & 0.372 \\
+ 0.509 & 0.965 & 0.115 \\
+ 0.383 & 0.652 & 0.803 \\
+ 0.591 & 0.412 & 0.019 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $1.8$ 
+Volume: $0.16$ 
+Surface Area: $1.75$

pretraining/mathematica/geometry/solids/56783.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.622 & 0.947 & 0.1 \\
+ 0.34 & 0.029 & 0.712 \\
+ 0.797 & 0.18 & 0.316 \\
+ 0.437 & 0.733 & 0.475 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.01$ 
+Surface Area: $0.72$ 
+Solid Angle: $0.08$

pretraining/mathematica/geometry/solids/57100.txt

@@ -0,0 +1,99 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ -2.412 & 0. & -0.843 \\
+ -2.412 & 0. & 0.157 \\
+ -2.285 & -0.934 & -0.509 \\
+ -2.285 & -0.934 & 0.491 \\
+ -2.285 & 0.934 & -0.509 \\
+ -2.285 & 0.934 & 0.491 \\
+ -2.157 & 0. & 0.824 \\
+ -2.079 & -0.577 & -1.588 \\
+ -2.079 & 0.577 & -1.588 \\
+ -1.951 & -1.512 & -1.255 \\
+ -1.951 & -1.512 & -0.255 \\
+ -1.951 & 1.512 & -1.255 \\
+ -1.951 & 1.512 & -0.255 \\
+ -1.745 & 0. & -2.333 \\
+ -1.618 & -0.934 & -2. \\
+ -1.618 & -0.934 & 1.236 \\
+ -1.618 & 0.934 & -2. \\
+ -1.618 & 0.934 & 1.236 \\
+ -1.539 & -1.512 & 0.824 \\
+ -1.539 & 1.512 & 0.824 \\
+ -1.491 & 0. & 1.569 \\
+ -1.206 & -2.089 & -0.921 \\
+ -1.206 & -2.089 & 0.079 \\
+ -1.206 & 2.089 & -0.921 \\
+ -1.206 & 2.089 & 0.079 \\
+ -1.079 & -1.868 & -1.588 \\
+ -1.079 & 1.868 & -1.588 \\
+ -0.873 & -1.512 & 1.569 \\
+ -0.873 & -0.357 & -2.667 \\
+ -0.873 & 0.357 & -2.667 \\
+ -0.873 & 1.512 & 1.569 \\
+ -0.745 & -1.291 & -2.333 \\
+ -0.745 & -0.577 & 1.903 \\
+ -0.745 & 0.577 & 1.903 \\
+ -0.745 & 1.291 & -2.333 \\
+ -0.539 & -2.089 & 0.824 \\
+ -0.539 & 2.089 & 0.824 \\
+ -0.333 & -2.446 & -1.255 \\
+ -0.333 & -2.446 & -0.255 \\
+ -0.333 & 2.446 & -1.255 \\
+ -0.333 & 2.446 & -0.255 \\
+ -0.127 & -0.934 & 1.903 \\
+ -0.127 & 0.934 & 1.903 \\
+ 0. & -1.868 & -2. \\
+ 0. & -1.868 & 1.236 \\
+ 0. & 0. & -3. \\
+ 0. & 0. & 2.236 \\
+ 0. & 1.868 & -2. \\
+ 0. & 1.868 & 1.236 \\
+ 0.127 & -0.934 & -2.667 \\
+ 0.127 & 0.934 & -2.667 \\
+ 0.333 & -2.446 & -0.509 \\
+ 0.333 & -2.446 & 0.491 \\
+ 0.333 & 2.446 & -0.509 \\
+ 0.333 & 2.446 & 0.491 \\
+ 0.539 & -2.089 & -1.588 \\
+ 0.539 & 2.089 & -1.588 \\
+ 0.745 & -1.291 & 1.569 \\
+ 0.745 & -0.577 & -2.667 \\
+ 0.745 & 0.577 & -2.667 \\
+ 0.745 & 1.291 & 1.569 \\
+ 0.873 & -1.512 & -2.333 \\
+ 0.873 & -0.357 & 1.903 \\
+ 0.873 & 0.357 & 1.903 \\
+ 0.873 & 1.512 & -2.333 \\
+ 1.079 & -1.868 & 0.824 \\
+ 1.079 & 1.868 & 0.824 \\
+ 1.206 & -2.089 & -0.843 \\
+ 1.206 & -2.089 & 0.157 \\
+ 1.206 & 2.089 & -0.843 \\
+ 1.206 & 2.089 & 0.157 \\
+ 1.491 & 0. & -2.333 \\
+ 1.539 & -1.512 & -1.588 \\
+ 1.539 & 1.512 & -1.588 \\
+ 1.618 & -0.934 & -2. \\
+ 1.618 & -0.934 & 1.236 \\
+ 1.618 & 0.934 & -2. \\
+ 1.618 & 0.934 & 1.236 \\
+ 1.745 & 0. & 1.569 \\
+ 1.951 & -1.512 & -0.509 \\
+ 1.951 & -1.512 & 0.491 \\
+ 1.951 & 1.512 & -0.509 \\
+ 1.951 & 1.512 & 0.491 \\
+ 2.079 & -0.577 & 0.824 \\
+ 2.079 & 0.577 & 0.824 \\
+ 2.157 & 0. & -1.588 \\
+ 2.285 & -0.934 & -1.255 \\
+ 2.285 & -0.934 & -0.255 \\
+ 2.285 & 0.934 & -1.255 \\
+ 2.285 & 0.934 & -0.255 \\
+ 2.412 & 0. & -0.921 \\
+ 2.412 & 0. & 0.079 \\
+\end{array}
+\right)$. Determine the EdgeCount.
+Answer:
+$180.$

pretraining/mathematica/geometry/solids/57829.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.618 & 0.681 & 0.011 \\
+ 0.231 & 0.142 & 0.098 \\
+ 0.545 & 0.928 & 0.645 \\
+ 0.592 & 0.199 & 0.044 \\
+ 0.806 & 0.685 & 0.606 \\
+ 0.205 & 0.447 & 0.383 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.06$ 
+Surface Area: $1.03$ 
+Solid Angle: $1.3$

pretraining/mathematica/geometry/solids/58247.txt

@@ -0,0 +1,15 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.836 & 0.08 & 0.111 \\
+ 0.551 & 0.149 & 0.582 \\
+ 0.443 & 0.924 & 0.401 \\
+ 0.213 & 0.885 & 0.461 \\
+ 0.834 & 0.837 & 0.845 \\
+ 0.463 & 0.242 & 0.691 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.35$ 
+Surface Area: $1.24$ 
+Volume: $0.08$

pretraining/mathematica/geometry/solids/60347.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.074 & 0.896 & 0.412 \\
+ 0.057 & 0.026 & 0.731 \\
+ 0.367 & 0.498 & 0.134 \\
+ 0.08 & 0.098 & 0.387 \\
+ 0.311 & 0.071 & 0.825 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.04$ 
+Surface Area: $0.83$ 
+Solid Angle: $0.28$

pretraining/mathematica/geometry/solids/60963.txt

@@ -0,0 +1,14 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.288 & 0.425 & 0.06 \\
+ 0.417 & 0.673 & 0.696 \\
+ 0.464 & 0.186 & 0.382 \\
+ 0.374 & 0.067 & 0.563 \\
+ 0.615 & 0.847 & 0.699 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $0.61$ 
+Solid Angle: $0.3$ 
+Volume: $0.02$

pretraining/mathematica/geometry/solids/61810.txt

@@ -0,0 +1,16 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.916 & 0.207 & 0.873 \\
+ 0.766 & 0.053 & 0.573 \\
+ 0.981 & 0.135 & 0.814 \\
+ 0.115 & 0.69 & 0.991 \\
+ 0.912 & 0.553 & 0.574 \\
+ 0.072 & 0.65 & 0.319 \\
+ 0.226 & 0.412 & 0.843 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.09$ 
+Surface Area: $1.37$ 
+Solid Angle: $2.32$